Detecting the presence and types of particle and other types of contaminants or irregularities on surfaces may be useful in many fields. For example, for a space telescope, it may be desirable to be able to detect the presence of dust particles on the surface of a telescope mirror and to be able to distinguish such particles from other imperfections such as micro-meteorite impacts or other defects.
In a more down-to-earth application, in semiconductor manufacturing, it may be useful to be able to detect the presence of contaminant particles on semiconductor wafers and surfaces prior to and during processing. Moreover, it may be useful to be able to distinguish such contaminate particles from surface defects (e.g., pits, crystal defects, and the like) in a semiconductor surface.
Light scattering provides a non-invasive method of analyzing high-quality substrates. Consequently, a great deal of effort has gone into developing theories to predict the scatter from simple contaminants in contact with a substrate. In these theories, an interaction field is generally introduced which is equivalent to the scattered field from the image of the contaminant. The boundary conditions can then be satisfied at the surfaces of the contaminant and the substrate simultaneously. Although in principle the scatter from any contaminant can be solved numerically, it is difficult to characterize contaminants from their resulting scatter.
There have been many experimental and modeling investigations in the prior art to attempt to discover and exploit the behavior of the polarization state of light scattered by particles. The 16-element light-scatter Mueller matrix is a useful tool in polarization analyses because it contains all the scattering information from a scattering system. The polarization elements of this matrix are extremely sensitive to small surface irregularities and can be used to characterize gross properties of a scattering system.
The use of polarized light to investigate particles has been attempted in the art. However, due to the irregular surface structure of particles, effectively modeling scatter response from different particle types and sizes so as to be able to characterize different particle sizes has heretofore been unknown in the art.